Corresponding author:
Professor Nick Glozier
Faculty of Medicine and Health,
University of Sydney,
NSW 2050,
Australia
email: nick.glozier@sydney.edu.au
| Draft | 12 March, 2021 |
| Words | 4395 |
| Tables | 0 |
| Figures | 4 |
keywords: Subjective wellbeing, household income, HILDA
A fundamental question for society is how much happiness does a dollar buy? The accepted view is that income and happiness increase together up to a point, after which there is little further gain from increasing wealth. While the location of this change point reportedly ranges between USD$60K to $95K, there has been no investigation as to whether this has increased or decreased over time. We determined the change over time in the relationship between income and both affective wellbeing (happiness), and cognitive wellbeing (life satisfaction), using household economic data from Australia between 2001-2019. The change point in the slope between happiness and income has increased over those 19 years faster than the cost of living, but the association of life satisfaction with income has remained linear. As a result, the happiness of a larger proportion of the population is more dependent on differences in income, despite stable differences in income distribution (e.g., Gini coefficient) in that time. This suggests that inequalities in income may be driving increasing inequities in happiness between the rich and the poor, with implications for health and recent government policy-goals to monitor and improve wellbeing.
Income has decreasing returns on happiness, across countries, cultures and ethnicities, with an inflection or change point near USD75,000. Below this point, happiness is relatively dependent on income levels; revealing an inequity in the distribution of happiness between rich and poor. We do not know whether or how this point changes over time. Has it decreased and reduced inequity, or increased the difference between the rich and poor? We examine 19 years of data from Australia and determine that the income level at which happiness becomes less influenced by income has increased, relative to the cost of living. The happiness of an increasing proportion of the population is more dependent on their financial security than ever this millennium. (120 max)
A fundamental question for governments and people is just how much wellbeing does a dollar buy? Increasing income is commonly associated with increasing happiness and subjective wellbeing, however a point at which subjective wellbeing no longer increases with income has also been widely observed (Clark et al., 2008; Dolan et al., 2008; Easterlin, 1974). Given that a central goal of nations and governments is to improve income under the assumption that higher income always increases wellbeing, challenges to this notion have far reaching consequences (Frijters et al., 2020; Laws and Monitor, 2014).
Subjective wellbeing is not a unitary entity (Diener et al., 2017); studies typically distinguish between life satisfaction, the cognitive appraisal of one’s own accomplishments, and affective wellbeing, one’s prevailing affective state, emotional mood, or everyday experience of happiness. Money can have different effects on each. For instance, we have recently reported that large increases in wealth, such as a major financial windfall, have a greater impact on an individual’s life satisfaction than their happiness (Kettlewell et al., 2020). The distinct effect of money on satisfaction and happiness was observed within individuals over time, however a distinct effect of income has also been observed between people with different income levels. For instance, Kahneman & Deaton (2010) showed that self-reported levels of happiness increased with household income up to a point (USD75,000), but after that, increasing income had little further effect on happiness. Conversely life satisfaction continued to increase with income beyond USD75,000. Indeed, the difference between the two questions: “How satisfied are you with your life?” and “How happy are you these days?” has been identified as a crucial mediating factor in a meta-analysis of 111 studies on income and wellbeing (Howell and Howell, 2008; also Veenhoven and Hagerty, 2006). Larger and newer data sets now also suggest that higher incomes are associated with more happiness and life satisfaction both within and across nations (Jebb et al., 2018; Killingsworth, 2021; Sacks et al., 2012). Results such as these have provided a more nuanced view of the relationship between income and wellbeing; namely that while both happiness and satisfaction continue to increase with income, the happiness returns are decreasing (Diener et al., 2010; Haushofer and Fehr, 2014).
Fundamentally, the existence of a change point in the relationship between income and happiness reveals an unacknowledged source of inequality in the distribution of wellbeing (i.e., happiness) in the economy. For instance, the change point of USD75,000 reported by Kahneman in 2008 was substantially more than the US median income of USD52,000 in the same year, indicating that the happiness of the poorest majority of the US population was tied to marginal changes in income while the happiness of a richer minority was not. Thus the change point represents the dollar value up to which income drives inequities in the distribution of happiness, such that a lower valued change point represents a more equitable distribution of happiness in the economy. Inequities in the distribution of wellbeing are increasingly relevant to governments and policy-makers due to the growing recognition that increasing income does not necessarily lead to equal changes in wellbeing (Clark, 2018; Frijters et al., 2020). Even prior to COVID-19, the World Gallup Poll has observed that happiness has been decreasing over the past decade in western Europe, North America, Australia and New Zealand, despite increases in income in the same countries (Sachs et al., 2019). However to date there has been no investigation of whether the relationship between income and happiness has changed over time which may contribute to these social trends. In particular has the change point between income and happiness increased or decreased, and therefore the distribution of happiness between rich and poor, become more or less equitable in the last two decades?
We used household economic panel data from Australia to provide the first investigation of whether changes in income and wellbeing have shifted the change point between 2001 to 2019. Australia is a developed western nation that has experienced a relatively stable period of economic growth in the last 19 years, which makes it a good candidate to observe how the function between income and subjective wellbeing has evolved over time without major economic shocks. HILDA (the Household, Income, and Labour Dynamics in Australia survey) provides a representative sample of households in Australia with detailed measurements of income and subjective wellbeing each year, which makes it an excellent data source to investigate the present question. We distinguished between satisfaction and happiness as different components of subjective wellbeing, and evaluated how each varied with household income over time using piecewise linear regression to determine the change points in each year.
To allow comparison with other major studies of income and wellbeing we used household after-tax income as the indicator of income and economic security (e..g, Kahneman and Deaton, 2010). Household income better represents economic security than personal income, since members of the same household share expenses as well as risks; i.e., they can provide a direct and immediate support network when financial shocks occur, which a priori might affect wellbeing. The ‘real household annual disposable income’ was calculated from the self-reported combined income of all household members after receipt of government pensions and benefits and deduction of income taxes in the financial year ended 30th June of the year of the wave (e.g., 2001 in wave 1). This was then adjusted for inflation - the rise in the general price level of the economy - using the Australian Bureau of Statistics (ABS) Consumer Price Index, so that income in all waves is expressed in 2019 prices, to give real income.
The equivalised household income was obtained by adjusting for household size (the number of adult and child household members). We used the ‘modified OECD’ scale (Hagenaars et al., 1994), which divides household income by 1 for the first household member plus 0.5 for each other household member aged 15 or over, plus 0.3 for each child under 15. A family comprising two adults and two children under 15 years of age would therefore have an equivalence scale of 2.1 (1 + 0.5 + 0.3 + 0.3), meaning that the family would need to have an income 2.1 times that of a single-person household in order to achieve the same standard of living. This scale recognises that larger households require more income, but it also recognises that there are economies of scale in consumption and that children require less than adults. The equivalised income calculated for a household is then assigned to each member of the household.
There are a variety of variables related to subjective well-being collected annually in HILDA, but the two we used here matched the variables we used in our previous paper (Kettlewell et al., 2020), namely, life satisfaction as a measure of cognitive wellbeing, and item 9 from the SF-36 (9a-9i) as a measure of affective wellbeing or happiness.
Life satisfaction (losat) was assessed by a single item question asked each survey: “All things considered, how satisfied are you with your life (0 to 10).”
Happiness was determined by 9 questions in the SF-36 (9a to 9i). The SF-36 is a widely used self-completion measure of various aspects of physical, emotional and mental health (Ware Jr, 2000). A subset of 9 questions assess mental health and vitality, with five questions measuring positive and negative aspects of mental health (e.g., “Felt so down in the dumps nothing could cheer me up,” “Been happy”), and four questions on positive and negative aspects of vitality (e.g., “feel full of life,” “felt worn out”). The response scale timeframe is the past four weeks and agreement was indicated on a six-point Likert scale. We reverse scored negatively phrased questions and calculated the sum of the nine questions so that higher scores represented better wellbeing. To aid interpretability, we rescaled the final sum to a score between 1-100, where 100 represents the maximum happiness achievable.
We modelled the relationship between income and each wellbeing variable (happiness and satisfaction) using a simple linear model and a piecewise model with a single change-point. The piecewise model was chosen as the simplest extension of a linear model which can identify a change point (inflection) in the relationship between wellbeing and income. The location of the change point was a free parameter which revealed where wellbeing no longer increased at a uniform rate with income. We then compared the linear model against the piecewise model to determine if a change point existed in any year between household income and each wellbeing variable (see Model Selection). Finally, where a change point existed, we determined the location of the change point for that year (see Parameter Estimation).
For modelling, both measures of wellbeing and income were rescaled with a mean of zero and a SD of 1 (z-scores) for each year.
Model Design
We adopted a Bayesian approach for estimating the linear and piecewise model in the software Stan (Bürkner, 2017; Stan Development Team, 2019). In each case the linear model was estimated as:
\[ y_i \sim N(\mu_i, \sigma^2_y) \]
\[ \mu_i = \beta_0 + \beta_1 X_i \]
Where \(X_i\) was an individual’s household income ($) as well as other covariates (age, age2, sex, education, chronic illness), and \(y_i\) was an individual’s wellbeing.
The piecewise model was a simple extension of this to include a free parameter to represent the changepoint in income (\(\omega\)) as well as the slope before the change point (\(\beta_1\)) and the slope after the change point (\(\beta_2\)):
\[ \mu_i = \beta_0 + \beta_1 (x_i - \omega) (x_i ≤ \omega) + \beta_2 (x_i - \omega) (x_i > \omega) + \beta_3 X_i \]
Where \(x_i\) was an individual’s household income, and \(X_i\) were the cross-sectional HILDA population weights to adjust for differences in the sample representativeness according to sex by broad age, marital status, region, and labour force status.
The above models estimated population-level effects separately for each year (t = 2001…2019). Because we were interested in the location of the change point between income and wellbeing that existed across individuals within each year, we ignored the panel design of HILDA because the dependency between observations of the same person across years was orthogonal to our effects of interest.
The parameters of the piecewise model used Gaussian priors centred at zero, with a regularized parameterization for the slopes and intercept of Normal(0, 0.1) for each β prior, and a slightly less restrictive regularization for the change point prior Normal(0, 0.5). These regularizing priors were selected to reduce overfitting while still allowing the model to learn the regular features of the sample, and so provide a more robust population estimate. They are skeptical priors and a prior predictive check confirmed they assume no relationship between income and wellbeing, with no difference in gradient before or after the change point (Supplementary materials, Figure S4).
Model Selection
To determine whether wellbeing was a linear or non-linear (e.g., piecewise) function of income, we compared the out-of-sample deviance of the linear and piecewise model fits using the Widely Applicable Information Criterion (WAIC). The WAIC is the log-posterior predictive density plus a penalty proportional to the variance in the posterior distribution, so it represents an approximation of the out-of-sample deviance that converges to the cross-validation accuracy in a large sample, with a penalty for the effective number of parameters (degrees of freedom). Thus using the out-of-sample deviance for model selection in combination with regularizing priors in our model design is a dual strategy to reduce overfitting and penalize overfitting. This makes it a useful approach for comparing models of varying complexity, such as our linear and piecewise (nonlinear) models. As with other deviance metrics, smaller negative WAIC values are better (i.e., indicate more accuracy).
WAIC was defined as: WAIC = -2(lppd - pWAIC)
Where lppd (log pointwise predictive density) is the total across observations of the log of the average likelihood of each observation, and pWAIC is the effective number of free parameters determined by the sum of the variance in log-likelihood for each observation (i).
Parameter Estimation
To determine the location of the change point (ω) between wellbeing and income, we modelled the relationship between income and wellbeing across individuals using the piecewise model described above, and sampled the posterior probability of ω over 4000 interations. The complete posterior distribution of ω for each year is presented along with the expected value (mean).
Covariates
Cross-sectional population weights for Australia provided by the University of Melbourne for each year were included as a covariate to adjust for differences in the sample representativeness. Full-time students were removed, as well as individuals with an annual household disposable income that was negative or indicated as topcoded by the University of Melbourne.
The broad demographic characteristics of the sample are presented in Supplementary Materials Table S1. Household income and average life satisfaction levels increased between 2001-2019, while average happiness scores decreased slightly over the 19 years. The proportions of each sex and couples were stable over time, as were the average household size and SEIFA index. However age, education, and chronic health conditions tended to slightly increase over time. For instance, average age increased by 2.3 years over the 19 years of the survey, which is obviously less than would occur in a cohort study (Watson and Wooden, 2012). Changes in the workforce varied with economic circumstances.
The relationship between household income and happiness (red) and satisfaction (blue) every four years is shown in Figure 1. For each wellbeing variable we show the results of a linear fit (rows 1 and 3) and a piecewise fit (rows 2 and 4). For visualization purposes only, we display the mean levels of income and wellbeing for each (equal-sized) income decile, whereas the line-of-best-fit and 95% credible intervals (shaded) in each regression model are derived from the underlying individual data-points.
Figure 1 legend: The relationship between income and wellbeing across equal-sized income deciles, overlaid by regression lines from linear and piecewise models (±95%CI). Wellbeing was measured as happiness (red) or life satisfaction (blue). The total number of individuals contributing to each regression in each year are noted (n).
The nonlinear relationship between happiness and income (Figure 1, 2nd row) was consistently and negatively inflected (happiness increased less with income after the change point). By contrast the nonlinear relationship between satisfaction and income shown in the 4th row exhibited negative inflection (2001, 2015, 2019), positive inflection (2005), and no apparent inflection (2010).
The evidence from model selection revealed the nonlinear (piecewise) fit of happiness, but not satisfaction, was superior to a linear fit in each year (Supplementary Materials, Figure S1). The WAIC difference indicated the piecewise fit of happiness had reliably less deviance than the linear fit, indicating the piecewise model predicted happiness from income more accurately using this out-of-sample metric. Overall the model comparison suggested that happiness and satisfaction have distinct relationships with household income; satisfaction tends to increase linearly with income, while a change point exists in the relationship between happiness and household income.
Figure 2 below presents the posterior distribution of each parameter from the piecewise model regressing happiness on income: the change point (ω), the intercept (β0), the pre-change point slope (β1), and the post-change point slope (β2). Over 4,000 samples were drawn from each piecewise model to determine the posterior distribution of each parameter (smallest bulk effective sample size = 661, see Table S2 for the complete fit statistics in Supplementary materials). Horizontal bars represent the 95% credible interval of the posterior distribution and so intervals which fall completely to the right of the vertical grey dotted line are credibly higher than the expected value of our base year, 2001.
Figure 2 legend: Posterior distributions of the change point parameter representing the location in real household income (real 2019 dollars), as well as the intercept, pre-slope and post-slope parameters in SD units (happiness). Horizontal bar represents the 95% credible region and the solid point indicates the expected value (median) of each distribution. Vertical dotted line indicates the 2001 expected value (median) as a base year comparison.
The posterior estimates of the change point in the association between happiness and household income indicates that the probable location (i.e., the real income value) of the change point shows a systematic increasing trend since 2001. Changes to the other parameters of the function between income and happiness also occurred between 2001 and 2019 (i.e., the pre-slope, post-slope and intercept), but did not show any sustained trend over the period.
Both the pre-slope and post-slope parameters (β1 and β2) were credibly larger than zero in each year, indicating there was a reliable dependency between happiness and income at income levels both below and above the change point. However the pre-slope parameter was in general four to five times greater than the post-slope values, indicating that the relationship between happiness and income among people in lower income households was an order of magnitude stronger than those in high income households.
Changes in the other demographic variables (e.g., age, education levels and chronic illness) did not materially alter the trends just described. The parameters of conditional piecewise models which included age, age2, education, and illness as covariates are compared in Supplementary materials (Figure S2).
The change in parameter values between 2001 to 2019 indicates the relationship between happiness and income has evolved over time. We determined the impact of this evolution on the distribution of happiness over the range of household income in 2019 in a counterfactual analysis. The counterfactual analysis is a hypothetical demonstration of how happiness would change if people in 2019 were subject to the function that existed in 2001, i.e., would happiness increase or decrease if the 2001 function was in place in 2019? This controls for changes in the sample which occur over time that are not related to happiness but could nevertheless contribute to changes in the distribution of happiness. For example, an increase in the range of (real) income levels in the economy between 2001 and 2019 could produce an increasing gap in happiness between the rich and poor - even with a stable relationship between income and happiness. Such changes in the sample characteristics may mask or confound the impact of the change point on the distribution of happiness without careful control. Because we were interested in the implications of the evolution of the function rather than changes in our sample characteristics per se, we estimated happiness levels for each person in 2019 (n = 14,459) using the 2001 function. These 2001 model-estimates were compared to (subtracted from) the 2019 model-estimates generated from the same sample (n = 14,459), to obtain the change (delta) in happiness for each person under the counterfactual. This delta is attributable to the evolution of the function between 2001 and 2019. Figure 3 below presents the 14,459 deltas from such a comparison, along with a smoothed mean (solid line) to summarize how the distribution of happiness evolved across the income range.
Figure 3 legend: The difference (∆) in predicted happiness between 2019 and 2001 for the same n = 14,459 individuals from the 2019 survey. Values below zero on the y-axis indicate lower happiness predictions using the 2019 model compared to using the 2001 model. Solid line overlay represents the (loess) smoothed average delta over the income distribution. Variance in these posterior samples is from the sample weights, uncertainty in the model parameters as well as observation-level (residual) variance.
Figure 3 shows that, on average, predicted happiness is higher for people with household incomes above $50K under the 2019 function, when compared to the function from 2001. This is indicated by the average delta (solid line) falling above zero on the right side of the plot. Conversely, people with household incomes below $50K, on average, had a decrease in predicted happiness under the 2019 function compared to 2001 function. Of course the obtained deltas are due to changes in all the parameters of the function, including the slope before and after the change point. However because this comparison was performed on the same individuals from the 2019 survey, it held characteristics such as age, income, etc, constant that would otherwise be expected to change over time and possibly contribute to any difference in happiness distribution. In this way these results isolate the amount of change entirely due to the evolution of the function between 2001 and 2019, and demonstrates how this has contributed to a more unequal distribution of happiness between the rich and the poor over time in Australia.
Any increase in the change point is likely to reduce the number of people who fall above it over time if this is greater than any increase in median income; i.e., over time a larger proportion of the population’s happiness is responsive to marginal changes in their income than previously. Figure 4 presents median household income levels weighted for the Australian population (by age, sex, marital status, labour force participation and geographical region). This shows the change point between income and happiness increased faster than rises in median household income between 2001 and 2019. The third panel shows that as a result, a smaller proportion of the Australian population in 2019 had a household income above the changepoint than in 2001.
Figure 4 legend: Real household income has stagnated in Australia since 2009 (post GFC) while the change point between happiness and income has increased.
This analysis of the Australian population since the millennium confirms previous findings (e.g., Howell and Howell, 2008; Kahneman and Deaton, 2010), that the relationship between the two types of subjective wellbeing and household income was positive but quite different: Satisfaction increased linearly with income, while happiness increased relatively steeply up to a point after which higher levels of income were associated with much more modest differences. We refer to the change point after which increases in income correspond to smaller increases in happiness as the cost of happiness. After this point, happiness is no longer as responsive to differences in household income, and the economic security it represents. Presumably after this point further increases in happiness depend more on other life factors (e.g., leisure time, social connections) than financial security. Our novel finding was that this change point in the relationship between household income and happiness increased faster than both inflation and median household income between 2001 and 2019. For the first time we have shown there has been a temporal shift in the change point between income and happiness over the 19 year period, such that happiness of an increasing proportion of the population has become more responsive to differences in income - especially the poor and middle-income earners.
Life satisfaction on the other hand appeared to show consistent increases with household income and we found no evidence of any change point. The difference may reflect the importance of a numerical dollar value (e.g., bank balance, house value) when cognitively appraising one’s life achievements, versus the relevance of that number to our everyday experience of joy and our prevailing mood.
An implication of the changing relationship between happiness and income is that income inequality may be driving increasing inequities in wellbeing. This is demonstrated in Figure 3, where the difference in predicted happiness between 2001 and 2019 increased for incomes above $50K/year and decreased for incomes below that level (see also Figure S6 in Supplementary materials). The inequity was also highlighted in Figure 4 where the change point of happiness represented a 9% increase over median income in 2001, while in 2019 it represented a 42% increase over median income. This increase relative to median income also represented a reduction from 43% to 26% in the proportion of people whose income fell above the changepoint. Thus we can see that over the last nineteen years the difference in income-related happiness between the rich and the poor has increased; while the happiness of an increasing proportion of people, including the middle-class, is more dependent on their financial security.
Australia has low levels of income disparity relative to many other OECD countries, and the Gini coefficient has changed little between 2001 and 2019 (APC, 2018), suggesting income inequality has remained steady over this time period. Our results do not conflict with this conclusion. Rather we are revealing that even a static income distribution may have dynamic effects on happiness over time. This highlights the issue that while traditional univariate measures of wealth and income inequality may be relatively stable and exhibit little change, their impact on wellbeing and health can still vary. As such, these results may well have relevance to other developed nations in North America and Europe which also enjoy low levels of income inequality, but have stagnating incomes, and declining happiness levels (Sachs et al., 2019). As focus shifts from traditional financial indicators towards health and wellbeing measures, findings such as this may become more prevalent.
The relationship between happiness and income is often described as log-linear (e.g., Kahneman and Deaton, 2010; Killingsworth, 2021). Under this view, similar proportional changes in income produce similar evaluations of satisfaction or happiness, rather than the absolute change. Likewise, the piecewise model reported here has a slope that reduces with income, albeit with a single identifiable change-point rather than a smooth curve. However our main thesis is not committed to a function with a single or smooth changepoint; only that the slope between income and happiness is unequal at different levels of income, and the function is shifting to the right over time (e.g., Figure 2). The choice between functions is somewhat arbitrary, since a log-linear function is as easily consistent with our thesis as the piecewise function we describe. Nevertheless, the model evidence favoured a piecewise- over a log-linear function in a supplementary analysis (Figure S3), which supports our model choice here.
Some recent studies have challenged the notion that the positive effect of income plateaus after some level (“satiety”) (Killingsworth, 2021; Stevenson and Wolfers, 2013; Twenge and Cooper, 2020). Our results also do not support a “satiety” point or flat gradient between income and happiness, as the average post-change slope between 2001-2019 was reliably above zero. The pre-change slope however was also four to five times greater than that, and we argue this difference in slopes indicates a previously unacknowledged inequity in the distribution of happiness between the rich and poor.
While the amount of variance in happiness explained by household income is small (Table S4, Supplementary materials), the slope is reliably above zero and small changes in happiness over an entire population will aggregate. Moreover, financial gains have one of the largest impacts on individual happiness in within-subject models (e.g., fixed-effects), second only to marriage by our estimate (Kettlewell et al., 2020), and there are many reasons why cross-sectional estimates of the covariance would under-represent this. Finally, happiness is measured on a subjective scale, where small changes at different points on the scale may represent a large change in some other functional/real-world outcome (e.g., risk of suicide). Ultimately, the real-world impact of small changes in a subjective measure such as happiness is inherently difficult to determine. Our aim here was to determine whether the relationship between income and happiness is changing at all, and whether this may be contributing to increasing inequity, and our results indicate this is the case.
As governments and policy-makers begin to focus on wellbeing, it will be critical to understand how traditional economic indicators such as household income, wealth inequality, and consumption interact with wellbeing and health. According to Frijters et al. (2020), coming up with a consensus to translate income into wellbeing features high on the wider wellbeing research agenda. Establishing the links between wealth, household income, wellbeing and health, and how inequalities in one drives inequities in the other, will be a critical step in that agenda.
This research was not supported by any funding.
The authors declare no competing interests.
This paper uses unit record data from Household, Income and Labour Dynamics in Australia Survey HILDA conducted by the Australian Government Department of Social Services (DSS). The findings and views reported in this paper, however, are those of the author[s] and should not be attributed to the Australian Government, DSS, or any of DSS’ contractors or partners. All code and scripts used in the analysis are available at https://github.com/datarichard/The-increasing-cost-of-happiness
Supplementary information is available online.